Abstract
We generalize the voter model to include social forces that produce conformity among voters and avoidance of cognitive dissonance of opinions within a voter. The time for both conformity and consistency (which we call the exit time) is, in general, much longer than for either process alone. We show that our generalized model can be applied quite widely: it is a form of Wright’s island model of population genetics, and is related to problems in the physical sciences. We give scaling arguments, numerical simulations, and analytic estimates for the exit time for a range of relative strengths in the tendency to conform and to avoid dissonance.
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References
Axelrod, R.: The dissemination of culture: A model with local convergence and global polarization. J. Confl. Resolut. 41 (1997)
Bednar, J., Bramson, A., Jones-Rooy, A., Page, S.: Conformity, consistency, and cultural heterogeneity. Mimeo, University of Michigan (2006)
Ben-Naim, E., Frachebourg, L., Krapivsky, P.: Coarsening and persistence in the voter model. Phys. Rev. E 53(4) (1996)
Blythe, R.A.: The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population (2006). Q-bio.PE/0606037
Chave, J.: Neutral theory and community ecology. Ecol. Lett. 7, 241–253 (2004)
Clement, E., Leroux-Hugon, P., Sander, L.: Exact results for a chemical reaction model. Phys. Rev. Lett. 67(12) (1991)
Dornic, I., Chaté, H., Chave, J., Hinrichsen, H.: Critical coarsening without surface tension: The universality class of the voter model. Phys. Rev. Lett. 87(4) (2001)
Drouffe, J.M., Godrèche, C.: Phase ordering and persistence in a class of stochastic processes interpolating between the Ising and voter models. J. Phys. A 32 (1999)
Festinger, L.: A Theory of Cognitive Dissonance. Row, Peterson & Company (1957)
Frachebourg, L., Krapivsky, P.L.: Exact results for kinetics of catalytic reactions. Phys. Rev. E 53(4) (1996)
Glaeser, E., Sacerdote, B., Scheinkman, J.: Crime and social interactions. Q. J. Econ. 111 (1996)
Hubbell, S.P.: The Unified Neutral Theory of Biodiversity and Biogeography. Princeton University Press, Princeton (2001)
Kimura, M., Ohta, T.: The average number of generations until fixation of a mutant gene in a finite population. Genetics 61, 763–771 (1969)
Krapivsky, P.L.: Kinetics of monomer-monomer surface catalytic reactions. Phys. Rev. A 45(2) (1992)
Liggett, T.: Interacting Particle Systems. Springer, New York (1985)
Redner, S.: A Guide to First-Passage Processes. Cambridge University Press, New York (2001)
Rohlf, F.J., Schnell, G.D.: An investigation of the isolation-by-distance model. Am. Nat. 105(944) (1971)
van Kampen, N.G.: Stochastic Processes in Physics and Chemistry. North-Holland, Amsterdam (1992), Revised and enlarged edition
Wright, S.: Evolution in Mendelian populations. Genetics 16, 97–159 (1931)
Young, P.: Individual Strategy and Social Structure: An Evolutionary Theory. Princeton University Press, Princeton (1998)
Ziff, R.M., Gulari, E., Barshad, Y.: Kinetic phase transitions in an irreversible surface-reaction model. Phys. Rev. Lett. 65(24) (1986)
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Page, S.E., Sander, L.M. & Schneider-Mizell, C.M. Conformity and Dissonance in Generalized Voter Models. J Stat Phys 128, 1279–1287 (2007). https://doi.org/10.1007/s10955-007-9369-y
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DOI: https://doi.org/10.1007/s10955-007-9369-y